Polarization-modulating optical element

ABSTRACT

A polarization-modulating optical element consisting of an optically active crystal material has a thickness profile where the thickness, as measured in the direction of the optical axis, varies over the area of the optical element. The polarization-modulating optical element has the effect that the plane of oscillation of a first linearly polarized light ray and the plane of oscillation of a second line early polarized light ray are rotated, respectively, by a first angle of rotation and a second angle of rotation, with the first angle of rotation and the second angle of rotation being different from each other.

BACKGROUND OF THE INVENTION

The invention relates to an optical element that affects thepolarization of light rays. The optical element has a thickness profileand consists or comprises of an optically active crystal with an opticalaxis.

In the continuing effort to achieve structures of finer resolution inthe field of microlithography, there is a parallel pursuit ofsubstantially three guiding concepts. The first of these is to provideprojection objectives of very high numerical aperture. Second is theconstant trend towards shorter wavelengths, for example 248 nm, 193 nm,or 157 nm. Finally, there is the concept of increasing the achievableresolution by introducing an immersion medium of a high refractive indexinto the space between the last optical element of the projectionobjective and the light-sensitive substrate. The latter technique isreferred to as immersion lithography.

In an optical system that is illuminated with light of a definedpolarization, the s- and p-component of the electrical field vector, inaccordance with Fresnel's equations, are subject to respectivelydifferent degrees of reflection and refraction at the interface of twomedia with different refractive indices. In this context andhereinafter, the polarization component that oscillates parallel to theplane of incidence of a light ray is referred to as p-component, whilethe polarization component that oscillates perpendicular to the plane ofincidence of a light ray is referred to as s-component. The differentdegrees of reflection and refraction that occur in the s-component incomparison to the p-component have a significant detrimental effect onthe imaging process.

This problem can be avoided with a special distribution of thepolarization where the planes of oscillation of the electrical fieldvectors of individual linearly polarized light rays in a pupil plane ofthe optical system have an approximately radial orientation relative tothe optical axis. A polarization distribution of this kind willhereinafter be referred to as radial polarization. If a bundle of lightrays that are radially polarized in accordance with the foregoingdefinition meets an interface between two media of different refractiveindices in a field plane of an objective, only the p-component of theelectrical field vector will be present, so that the aforementioneddetrimental effect on the imaging quality is reduced considerably.

In analogy to the foregoing concept, one could also choose apolarization distribution where the planes of oscillation of theelectrical field vectors of individual linearly polarized light rays ina pupil plane of the system have an orientation that is perpendicular tothe radius originating from the optical axis. A polarizationdistribution of this type will hereinafter be referred to as tangentialpolarization. If a bundle of light rays that are tangentially polarizedin accordance with this definition meets an interface between two mediaof different refractive indices, only the s-component of the electricalfield vector will be present so that, as in the preceding case, therewill be uniformity in the reflection and refraction occurring in a fieldplane.

Providing an illumination with either tangential or radial polarizationin a pupil plane is of high importance in particular when putting theaforementioned concept of immersion lithography into practice, becauseof the considerable negative effects on the state of polarization thatare to be expected based on the differences in the refractive index andthe strongly oblique angles of incidence at the respective interfacesfrom the last optical element of the projection objective to theimmersion medium and from the immersion medium to the coatedlight-sensitive substrate.

U.S. Pat. No. 6,191,880 B1 discloses an optical arrangement forgenerating an approximately radial polarization. The arrangementincludes among other things a raster of half-wave plates whoserespective directions of preference are oriented so that when linearlypolarized light passes through the raster arrangement, the plane ofoscillation is rotated into the direction of a radius originating fromthe optical axis. However, because the raster arrangement is produced byjoining a large number of individually oriented half-wave plates, it isexpensive to produce. Furthermore, the change in the direction of thepolarization is constant within the area of each individual half-waveplate whose diameter is typically between 10 and 20 mm, so that nocontinuous radial polarization can be produced through this concept.

A birefringent element of crystalline quartz with an irregularly varyingthickness is proposed in DE 198 07 120 A1 for the compensation of localaberrations of a defined state of polarization in an optical system.However, the variation in thickness in a birefringent element of thistype leads to locally different states of polarization. In particular,the linear state of polarization is, as a rule, not preserved in anarrangement of this type.

OBJECT OF THE INVENTION

The present invention therefore has the objective to propose apolarization-modulating optical element which—with a minimum loss ofintensity—affects the polarization of light rays in such a way that fromlinearly polarized light with a first distribution of the directions ofthe oscillation planes of individual light rays, the optical elementgenerates linearly polarized light with a second distribution of thedirections of the oscillation planes of individual light rays.

Further objects of the present invention are to propose an opticalsystem with improved properties of the polarization-modulating opticalelement regarding thermal stability of the second distribution ofoscillation planes (polarization distribution), and to minimize theinfluence of additional optical elements in the optical system to thepolarization distribution after the light rays have passed theseelements.

SUMMARY OF THE INVENTION

To meet the foregoing objectives, a polarization-modulating opticalelement is proposed which consists or comprises of an optically activecrystal and which, according to the invention, is shaped with athickness profile that varies in the directions perpendicular to theoptical axis. Further, the optical systems as described in claims 57,64, 65, 70 and 75 meet the objects of the present invention. Additionalpreferred embodiments of the optical systems according to the presentinvention are given in the dependent claims.

A polarization-modulating optical element according to the invention hasthe effect that the plane of oscillation of a first linearly polarizedlight ray and the plane of oscillation of a second linearly polarizedlight ray are rotated, respectively, by a first and a second angle ofrotation, with the first angle of rotation being different from thesecond angle of rotation. According to the invention, thepolarization-modulating optical element is made of an optically activematerial.

Advantageous further developments of the inventive concept are describedhereinafter.

In order to generate from linearly polarized light an arbitrarilyselected distribution of linearly polarized light rays with a minimumloss of intensity, an optically active crystal with an optical axis isused as raw material for the polarization-modulating optical element.The optical axis of a crystal, also referred to as axis of isotropy, isdefined by the property that there is only one velocity of lightpropagation associated with the direction of the optical axis. In otherwords, a light ray traveling in the direction of an optical axis is notsubject to a linear birefringence. The polarization-modulating opticalelement has a thickness profile that varies in the directionsperpendicular to the optical axis of the crystal. The term “linearpolarization distribution” in this context and hereinafter is used withthe meaning of a polarization distribution in which the individual lightrays are linearly polarized but the oscillation planes of the individualelectrical field vectors can be oriented in different directions.

If linearly polarized light traverses the polarization-modulatingoptical element along the optical axis of the crystal, the oscillationplane of the electrical field vector is rotated by an angle that isproportional to the distance traveled inside the crystal. The sense ofrotation, i.e., whether the oscillation plane is rotated clockwise orcounterclockwise, depends on the crystal material, for exampleright-handed quartz vs. left-handed quartz. The polarization plane isparallel to the respective directions of the polarization and thepropagation of the light ray. In order to produce an arbitrarilyselected distribution of the angles of rotation, it is advantageous ifthe thickness profile is designed so that the plane of oscillation of afirst linearly polarized light ray and the plane of oscillation of asecond linearly polarized light ray are rotated, respectively, by afirst and a second angle of rotation, with the first angle of rotationbeing different from the second angle of rotation. By shaping theelement with a specific thickness at each location, it is possible torealize arbitrarily selected angles of rotation for the oscillationplanes.

Different optically active materials have been found suitable dependenton the wavelength of the radiation being used, specifically quartz,TeO₂, and AgGaS₂.

In an advantageous embodiment of the invention, thepolarization-modulating optical element has an element axis oriented inthe same direction as the optical axis of the crystal. In relation tothe element axis, the thickness profile of the optical element is afunction of the azimuth angle θ alone, with the azimuth angle θ beingmeasured relative to a reference axis that intersects the element axisat a right angle. With a thickness profile according to this design, thethickness of the optical element is constant along a radius thatintersects the element axis at a right angle and forms an azimuth angleθ with the reference axis.

In a further advantageous embodiment of the invention, an azimuthalsection d(r=const., θ) of the thickness profile d(r,θ) at a constantdistance r from the element axis is a linear function of the azimuthangle θ. In the ideal case, this azimuthal section has a discontinuityat the azimuth angle θ=0. The linear function d(r=const., θ) at aconstant distance r from the element axis has a slope

${{m} = \frac{180{^\circ}}{{\alpha\Pi}\; r}},$

wherein α stands for the specific rotation of the optically activecrystal. At the discontinuity location for 0=0, there is an abrupt stepin the thickness by an amount of 360°/α. The step at the discontinuitylocation can also be distributed over an azimuth angle range of a fewdegrees. However, this has the result of a non-optimized polarizationdistribution in the transition range.

In a further advantageous embodiment of the invention, an azimuthalsection d(r=const., θ) of the thickness profile d(r,θ) at a constantdistance r from the element axis is a linear function of the azimuthangle θ with the same slope m but, in the ideal case, with twodiscontinuities at the azimuth angles θ=0 and θ=180°, respectively. Ateach discontinuity location, there is an abrupt step in the thickness byan amount of 180°/α. The two abrupt steps at the discontinuity locationscan also be distributed over an azimuth angle range of a few degrees.However, this has the result of a non-optimized polarizationdistribution in the transition range.

In a further advantageous embodiment of the invention, an azimuthalsection d(r=const., θ) of the thickness profile d(r,θ) at a constantdistance r from the element axis and in a first azimuth angle range of10°<θ<170° is a linear function of the azimuth angle θ with a firstslope m, while in a second azimuth angle range of 190°<θ<350°, theazimuthal section is a linear function of the azimuth angle θ with asecond slope n. The slopes m and n have the same absolute magnitude butopposite signs. The magnitude of the slopes m and n at a distance r fromthe element axis is

${m} = {{n} = {\frac{180{^\circ}}{{\alpha\Pi}\; r}.}}$

With this arrangement, the thickness profile for all azimuth angles,including θ=0 and θ=180°, is a continuous function without abruptchanges in thickness.

In a further advantageous embodiment of the invention, thepolarization-modulating optical element is divided into a large numberof planar-parallel portions of different thickness or comprises at leasttwo planar-parallel portions. These portions can for example beconfigured as sectors of a circle, but they could also have a hexagonal,square, rectangular, or trapezoidal shape.

In a further advantageous embodiment of the invention, a pair of firstplan-parallel portions are arranged on opposite sides of a centralelement axis of said polarization-modulating optical element, and a pairof second plan-parallel portions are arranged on opposite sides of saidelement axis and circumferentially displaced around said element axiswith respect to said first plan-parallel portions, wherein each of saidfirst portions has a thickness being different from a thickness of eachof said second portions.

In a further advantageous embodiment of the invention, a plane ofoscillation of linearly polarized light passing through thepolarization-modulating optical element is rotated by a first angle ofrotation β₁ within at least one of said first plan-parallel portions andby a second angle of rotation β₂ within at least one of said secondplan-parallel portions, such that β₁ and β₂ are approximately conformingor conform to the expression |β₂−β₁|=(2n+1)·90°, with n representing aninteger.

In an advantageous embodiment, β₁ and β₂ are approximately conforming orconform to the expressions β₁=90°+p·180°, with p representing aninteger, and β₂=q·180°, with q representing an integer other than zero.As will discussed below in more detail, such an embodiment of thepolarization modulating optical element may be advantageously used inaffecting the polarization of traversing polarized light such thatexiting light has a polarization distribution being—depending of theincoming light—either approximately tangentially or approximatelyradially polarized.

The pair of second plan-parallel portions may particularly becircumferentially displaced around said element axis with respect tosaid pair of first plan-parallel portions by approximately 90°.

In a further advantageous embodiment of the invention, said pair offirst plan-parallel portions and said pair of second plan-parallelportions are arranged on opposite sides of a central opening or acentral obscuration of said polarization-modulating optical element.

Adjacent portions of said first and second pairs can be spaced apartfrom each other by regions being opaque to linearly polarized lightentering said polarization-modulating optical element. Said portions ofsaid first and second group can particularly be held together by amounting. Said mounting can be opaque to linearly polarized lightentering said polarization-modulating optical element. The mounting canhave a substantially spoke-wheel shape.

In a further advantageous embodiment of the invention, thepolarization-modulating optical element comprises a first group ofsubstantially planar-parallel portions wherein a plane of oscillation oftraversing linearly polarized light is rotated by a first angle ofrotation β₁, and a second group of substantially planar-parallelportions wherein a plane of oscillation of traversing linearly polarizedlight is rotated by a second angle of rotation, such that β₁ and β₂ areapproximately conforming or conform to the expression |₂−β₁=(2n+1)·90°,with n representing an integer.

In a further advantageous embodiment of the invention, β₁ and β₂ areapproximately conforming to the expressions β₁=90°+p·180°, with prepresenting an integer, and β₂=q·180°, with q representing an integerother than zero.

In a further advantageous embodiment of the invention, the thicknessprofile of the polarization-modulating optical element has a continuoussurface contour without abrupt changes in thickness, whereby anarbitrarily selected polarization distribution can be generated whosethickness profile is represented by a continuous function of thelocation.

To ensure an adequate mechanical stability of the optical element, it isimportant to make the minimal thickness d_(min) of thepolarization-modulating optical element at least equal to 0.002 timesthe element diameter D.

If the optically active material used for the optical element also hasbirefringent properties as is the case for example with crystallinequartz, the birefringence has to be taken into account for light rayswhose direction of propagation deviates from the direction of theoptical crystal axis. A travel distance of 90°/α inside the crystalcauses a linear polarization to be rotated by 90°. If birefringence ispresent in addition to the rotating effect, the 90° rotation will beequivalent to an exchange between the fast and slow axis in relation tothe electrical field vector of the light. Thus, a total compensation ofthe birefringence is provided for light rays with small angles ofincidence if the distance traveled inside the crystal equals an integermultiple of 180°/α. In order to meet the aforementioned requirement formechanical stability while simultaneously minimizing the effects ofbirefringence, it is of particular advantage if thepolarization-modulating optical element is designed with a minimumthickness of

${d_{\min} = {N \cdot \frac{90{^\circ}}{\alpha}}},$

where N represents a positive integer.

From a manufacturing point of view, it is particularly advantageous toprovide the optical element with a hole at the center or with a centralobscuration

For light rays propagating not exactly parallel to the optical crystalaxis, there will be deviations of the angle of rotation. In addition,the birefringence phenomenon will have an effect. It is thereforeparticularly advantageous if the maximum angle of incidence of anincident light bundle with a large number of light rays within a spreadof angles relative to the optical crystal axis is no larger than 100mrad, preferably no larger than 70 mrad, and with special preference nolarger than 45 mrad.

In order to provide an even more flexible control over a state ofpolarization, an optical arrangement is advantageously equipped with adevice that allows at least one further polarization-modulating opticalelement to be placed in the light path. This furtherpolarization-modulating optical element can be an additional elementwith the features described above. However, it could also be configuredas a planar-parallel plate of an optically active material or anarrangement of two half-wavelength plates whose respective fast and slowaxes of birefringence are rotated by 45° relative to each other.

The further polarization-modulating optical element that can be placedin the optical arrangement can in particular be designed in such a waythat it rotates the oscillation plane of a linearly polarized light rayby 90°. This is particularly advantageous if the firstpolarization-modulating element in the optical arrangement produces atangential polarization. By inserting the 90°-rotator, the tangentialpolarization can be converted to a radial polarization.

In a further embodiment of the optical arrangement, it can beadvantageous to configure the further polarization-modulating opticalelement as a planar-parallel plate which works as a half-wavelengthplate for a half-space that corresponds to an azimuth-angle range of180°. This configuration is of particular interest if the firstpolarization-modulating optical element has a thickness profile(r=const., θ) that varies only with the azimuth angle θ and if, in afirst azimuth angle range of 10°<θ<170°, the thickness profile(r=const., θ) is a linear function of the azimuth angle θ with a firstslope m, while in a second azimuth angle range of 190°<θ<350°, thethickness profile is a linear function of the azimuth angle θ with asecond slope n, with the slopes m and n having the same absolutemagnitude but opposite signs.

The refraction occurring in particular at sloped surfaces of apolarization-modulating element can cause a deviation in the directionof an originally axis-parallel light ray after it has passed through thepolarization-modulating element. In order to compensate this type ofdeviation of the wave front which is caused by thepolarization-modulating element, it is advantageous to arrange acompensation plate of a not optically active material in the light pathof an optical system, with a thickness profile of the compensation platedesigned so that it substantially compensates an angular deviation ofthe transmitted radiation that is caused by the polarization-modulatingoptical element. Alternatively, an immersion fluid covering the profiledsurface of the polarization-modulating element could be used for thesame purpose.

Polarization-modulating elements of the foregoing description, andoptical arrangements equipped with them, are advantageously used inprojection systems for microlithography applications. In particular,polarization-modulating elements of this kind and optical arrangementsequipped with them are well suited for projection systems in which theaforementioned immersion technique is used, i.e., where an immersionmedium with a refractive index different from air is present in thespace between the optical element nearest to the substrate and thesubstrate.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention will hereinafter be explained in more detail withreference to the attached drawings, wherein:

FIG. 1 illustrates a polarization-modulating optical element with athickness profile;

FIG. 2 schematically illustrates how the plane of oscillation is rotatedwhen a linearly polarized light ray propagates along the optical axis inan optically active crystal;

FIG. 3 illustrates a first exemplary embodiment of apolarization-modulating optical element;

FIG. 4 a schematically illustrates a second exemplary embodiment of apolarization-modulating optical element;

FIG. 4 b illustrates the thickness profile as a function of the azimuthangle in the embodiment of the polarization-modulating optical elementof FIG. 4 a;

FIG. 4 c illustrates the thickness profile as a function of the azimuthangle in a further embodiment of the polarization-modulating opticalelement;

FIG. 4 d illustrates the thickness profile as a function of the azimuthangle in the embodiment of the polarization-modulating optical elementof FIG. 3;

FIG. 4 e illustrates the thickness profile as a function of the azimuthangle in a further embodiment of the polarization-modulating opticalelement;

FIG. 4 f schematically illustrates a further exemplary embodiment of apolarization-modulating optical element;

FIG. 5 schematically illustrates the polarization distribution of abundle of light rays before and after passing through thepolarization-modulating optical element with the thickness profileaccording to FIG. 3 or 4 d;

FIG. 6 schematically illustrates the polarization distribution of abundle of light rays before and after passing through an opticalarrangement with the polarization-modulating optical element with thethickness profile according to FIG. 3 and a furtherpolarization-modulating optical element;

FIG. 7 a schematically illustrates the polarization distribution of abundle of light rays before and after passing through an opticalarrangement with the polarization-modulating optical element with thethickness profile according to FIG. 4 e and a planar-parallel plate, onehalf of which is configured as a half-wave plate;

FIG. 7 b shows a plan view of a planar-parallel plate, one half of whichis configured as a half-wave plate;

FIG. 8 schematically illustrates a microlithography projection systemwith a polarization-modulating optical element; and

FIG. 9 schematically shows a parallel plane plate of optical activematerial used as a polarization-modulating element by adjusting itstemperature and/or temperature profile;

FIG. 10 shows a combination of a parallel plate of optical activematerial with a plate made of birefringent material; and

FIG. 11 shows schematically a temperature compensatedpolarization-modulating optical element for the application in anoptical system.

PROVISIONAL DESCRIPTION OF PREFERRED EMBODIMENTS

FIG. 1 illustrates a polarization-modulating optical element 1 of anoptically active material. Particularly well suited for this purpose areoptically active crystals with at least one optical crystal axis whichare transparent for the wavelength of the light being used. For exampleTeO₂ works in a range of wavelengths from 1000 nm down to 300 nm, AgGaS₂works from 500 nm to 480 nm, and quartz from 800 nm down to 193 nm. Thepolarization-modulating optical element 1 is designed so that theelement axis is oriented parallel to the optical crystal axis. In orderto produce a selected polarization distribution, the optical element 1is designed with a thickness profile (measured parallel to the elementaxis EA) which varies in the directions perpendicular to the elementaxis EA, also comprising variations in thickness of the optical elementin an azimuth direction θ (see FIG. 3) at e.g. a fixed distance of theelement axis EA.

FIG. 2 will serve to explain the function of optically active crystals,and in particular of polarization-modulating elements made from suchcrystals, in more detail.

Optically active crystals have at least one optical axis OA which isinherent in the crystal structure. When linearly polarized light travelsalong this optical axis OA, the plane of oscillation of the electricalfield vector 206 is rotated by an angle β of proportionate magnitude asthe distance d traveled by the light inside the crystal 202. Theproportionality factor between distance d and angle of rotation is thespecific rotation α. The latter is a material-specific quantity and isdependent on the wavelength of the light rays propagating through thecrystal. For example in quartz, the specific rotation at a wavelength of180 nm was measured as about α=(325.2±0.5)°/mm, at 193 nm α=323.1°/mm ata temperature of 21.6° C.

It is also important for the present invention, applying opticallyactive materials in an illumination system and/or an objective of aprojection optical system of e.g. a projection apparatus used inmicrolithography, that also the temperature dependency of the specificrotation is considered. The temperature dependency of the specificrotation α for a given wavelength is to a good and first linearapproximation given by α(T)=α₀(T₀)+γ*(T−T₀), where γ is the lineartemperature coefficient of the specific rotation α. In this case α(T) isthe optical activity coefficient or specific rotation at the temperatureT and α₀ is the specific rotation at a reference temperature T₀. Foroptical active quartz material the value γ at a wavelength of 193 nm andat room temperature is γ=2.36 mrad/(mm*K).

Referring again to FIG. 2, in particular, light that propagates insidethe crystal 202 along the optical axis OA is not subject to a linearbirefringence. Thus, when a linearly polarized light ray traverses anoptically active crystal 202 along the optical axis OA, its state ofpolarization remains the same except for the change in the spatialorientation of the plane of oscillation of the electrical field vector206 which depends on the distance d traveled by the light ray inside thecrystal 202.

Based on this property of an optically active crystal, it is possible toproduce an arbitrarily selected linear polarization distribution bydesigning the polarization-modulating optical element 1 of FIG. 1 with athickness profile that varies dependent on the location. The thicknessprofile is designed to have the effect that the directions ofpolarization of parallel linearly polarized light rays are rotated by anangle that varies dependent on the location where the light raytraverses the optical element.

More general, alternative or in addition to the variation of thethickness d=d(x,y) of the polarization-modulating element, the specificrotation α may itself be dependent on the location within the modulatingelement such that a becomes an α(x,y,z) or α(r,θ,z), where x,y or r,θare Cartesian or polar coordinates in a plane perpendicular to theelement axis EA (or alternative to the optical axis OA) of thepolarization-modulating element, as shown e.g. in FIG. 1, where z is theaxis along the element axis EA. Of course also a description inspherical-coordinates like r,θ,φ, or others is possible. Taking intoaccount the variation of the specific rotation α, thepolarization-modulating optical element in general comprises a varyingprofile of the “optical effective thickness D” defined asD(x,y)=d(x,y)*α(x,y), if there is no dependency of α in z-direction. Inthe case that α may also depend on the z-direction (along the opticalaxis or element axis EA, or more general along a preferred direction inan optical system or a direction parallel to the optical axis of anoptical system) D has to be calculated by integrationD(x,y)=∫α(x,y,z)dz(x,y), along the polarization-modulating opticalelement. In general, if a polarization-modulating optical element isused in an optical system, having an optical axis or a preferreddirection defined by the propagation of a light beam through the opticalsystem, the optical effective thickness D is calculated by integratingthe specific rotation α along the light path of a light ray within thepolarization-modulating optical element. Under this general aspect thepresent invention relates to an optical system comprising an opticalaxis or a preferred direction given by the direction of a light beampropagating through the optical system. The optical system alsocomprises a polarization-modulating optical element described bycoordinates of a coordinate system, wherein one preferred coordinate ofthe coordinate system is parallel to the optical axis of the opticalsystem or parallel to the preferred direction. As an example, in theabove case this preferred direction was the z-coordinate which is thepreferred coordinate. Additionally the polarization-modulating opticalelement comprises optical active material and also a profile ofeffective optical thickness D as defined above, wherein the effectiveoptical thickness D varies at least as a function of one coordinatedifferent from the preferred coordinate of the coordinate systemdescribing the polarization-modulating optical element. In the aboveexample the effective optical thickness D varies at least as a functionof the x- or y-coordinate, different from the z-coordinate (thepreferred coordinate). There are different independent methods to varythe effective optical thickness of an optical active material. One is tovary the specific rotation by a selection of appropriate materials, orby subjecting the optically active material to a non-uniform temperaturedistribution, or by varying the geometrical thickness of the opticallyactive material. Also combinations of the mentioned independent methodsresult in a variation of the effective optical thickness of an opticalactive material.

FIG. 3 illustrates an embodiment of the polarization-modulating opticalelement 301 which is suited specifically for producing a tangentialpolarization. A detailed description will be presented in the context ofFIGS. 4 d and 5. The embodiment illustrated in FIG. 3 will serve tointroduce several technical terms that will be used hereinafter with thespecific meanings defined here.

The polarization-modulating optical element 301 has a cylindrical shapewith a base surface 303 and an opposite surface 305. The base surface303 is designed as a planar circular surface. The element axis EAextends perpendicular to the planar surface. The opposite surface 305has a contour shape in relation to the element axis EA in accordancewith a given thickness profile. The optical axis of the optically activecrystal runs parallel to the element axis EA. The reference axis RA,which extends in the base plane, intersects the element axis at a rightangle and serves as the reference from which the azimuth angle θ ismeasured. In the special configuration illustrated in FIG. 3, thethickness of the polarization-modulating optical element 301 is constantalong a radius R that is perpendicular to the element axis EA anddirected at an angle θ relative to the reference axis RA. Thus, thethickness profile in the illustrated embodiment of FIG. 3 depends onlyon the azimuth angle θ and is given by d=d(θ). The optical element 301has an optional central bore 307 coaxial with the element axis EA. In another preferred embodiment of the polarization-optical element thethickness may vary along the radius R such that the thickness profile isd=d(R,θ). In a further more generalized preferred embodiment thethickness profile shown in FIG. 3 is not representing the geometricalthickness d of the polarization-optical element, as described above, butthe profile represents the optical effective thickness D=D(R,θ)=D(x,y),depending on the used coordinate system. In this case also any profileof the specific rotation like e.g. α=α(x,y)=α(R,θ) orα=α(x,y,z)=α(R,θ,z) is considered in the profile of thepolarization-modulating optical element which is effective for a changein the direction of the polarization plane of a passed light beam.

In addition it should be mentioned that the polarization-modulatingoptical element 301 not necessary need to comprise a planar base surface303. This surface in general can also comprise a contour shaped surfacee.g. similar or equal to the surface as designated by 305 shown in FIG.3. In such a case it is of advantage to describe the contour surfaces303 and 305 relative to a plane surface perpendicular to the opticalaxis or element axis.

FIG. 4 a schematically illustrates a further embodiment of thepolarization-modulating optical element 401. The element axis EA throughthe center of the polarization-modulating optical element 401 in thisrepresentation runs perpendicular to the plane of the drawing, and theoptical crystal axis of the crystal runs parallel to the element axis.Like the embodiment of FIG. 3, the polarization-modulating opticalelement 401 has an optional central bore 407. Thepolarization-modulating optical element 401 is divided into a largenumber of planar-parallel portions 409 in the shape of sectors of acircle which differ in their respective thicknesses. Alternativeembodiments with different shapes of the portions 409 are conceivable.They could be configured, e.g., as hexagonal, square, rectangular ortrapeze-shaped raster elements.

As described in connection with FIG. 3, the embodiment according to FIG.4 a can be modified such that the different thicknesses of the sectorsshould be understood as different effective optical thicknesses D. Inthis case the specific rotation α may vary from one segment to the othertoo. To manufacture such an embodiment, the polarization-modulatingoptical element can e.g. have a shape as shown in FIG. 4 a in which thesectors 409 are at least partly exchanged e.g. by any optical inactivematerial, which is the simplest case to vary the specific rotation α tozero. Also as a further embodiment the sectors 409 may be replaced bycuvettes or cells which are filed with an optical active or opticalinactive liquid. In this case the polarization-modulating opticalelement may comprise optical active and optical inactive sections. Ifthe sectors 409 are only party replaced by cuvettes or if at least onecuvette is used in the polarization-modulating optical element 401, acombination of e.g. optical active crystals with e.g. optical active oroptical inactive liquids in one element 40 is possible. Such an opticalsystem according to the present invention may comprise apolarization-modulating optical element which comprises an opticallyactive or an optically inactive liquid and/or an optically activecrystal. Further, it is advantageously possible that thepolarization-modulating optical element of the optical system accordingto the present invention comprises clockwise and counterclockwiseoptically active materials. These materials could be solid or liquidoptically active materials. Using liquids in cuvettes has the advantagethat by changing the liquids, or the concentration of the optical activematerial within the liquid, the magnitude of the change in polarizationcan be easily controlled. Also any thermal changes of the specificrotation α due to the thermal coefficient γ of the specific rotation αcan be controlled e.g. by temperature control of the optical activeliquid such that either the temperature is constant within the cuvette,or that the temperate has predefined value T such that the specificrotation will have the value α(T)=α₀(T₀)+γ*(T−T₀). Also the formation ofa certain temperature distribution within the liquid may be possiblewith appropriate heating and/or cooling means controlled by controlmeans.

The optical systems in accordance with the present inventionadvantageously modify respective planes of oscillation of a firstlinearly polarized light ray and a second linearly polarized light ray.Both light rays propagating through the optical system, and being atleast a part of the light beam propagating through the optical system.The light rays are also passing the polarization-modulating opticalelement with different paths, and are rotated by a respective first andsecond angle of rotation such that the first angle is different of thesecond angle. In general the polarization-modulating optical element ofthe optical systems according to the present invention transform a lightbundle with a first linear polarization distribution, which enters saidpolarization-modulating optical element, into a light bundle exitingsaid polarization-modulating optical element. The exiting light bundlehaving a second linear polarization distribution, wherein the secondlinear polarization distribution is different from the first linearpolarization distribution.

FIG. 4 b shows the thickness profile along an azimuthal sectiond(r=const.,θ) for the polarization-modulating optical element 401divided into sectors as shown in FIG. 4 a. The term azimuthal section asused in the present context means a section traversing the thicknessprofile d(θ,r) along the circle 411 marked in FIG. 4 a, i.e., extendingover an azimuth angle range of 0°≦θ≦360° at a constant radius r. Ingeneral the profile shows the optical effective thickness D=D(θ) along acircle 411.

An azimuthal section of a polarization-modulating optical element 401that is divided into sector-shaped portions has a stair-shaped profilein which each step corresponds to the difference in thickness d oroptical effective thickness D between neighboring sector elements. Theprofile has e.g. a maximum thickness d_(max) and a minimum thicknessd_(min). In order to cover a range of 0≦β≦360° for the range of theangle of rotation of the oscillation plane of linearly polarized light,there has to be a difference of 360°/α between d_(max) and d_(min). Theheight of each individual step of the profile depends on the number n ofsector elements and has a magnitude of 360°/(n·α). At the azimuth angleθ=0°, the profile has a discontinuity where the thickness of thepolarization-modulating optical element 401 jumps from d_(min) tod_(max). A different embodiment of the optical element can have athickness profile in which an azimuthal section has two discontinuitiesof the thickness, for example at θ=0° and θ=180°.

In an alternative embodiment the profile has e.g. a maximum opticaleffective thickness D_(max) and a minimum optical effective thicknessD_(min), and the geometrical thickness d is e.g. constant, resulting ina variation of the specific rotation α of the individual segments 409 ofthe element 401. In order to cover a range of 0≦β≦360° for the range ofthe angle of rotation of the oscillation plane of linearly polarizedlight, there has to be a difference of 360°/d between α_(max) andα_(min). The change of the specific rotation of each individual step ofthe profile depends on the number n of sector elements 409 and has amagnitude of 360°/(n·d). At the azimuth angle θ=0°, the profile has adiscontinuity regarding the optical effective thickness where it jumpsfrom D_(min) to D_(max). It should be pointed out, that advantageouslyin this embodiment there is no discontinuity in the geometricalthickness d of the polarization-modulating element 401. Also thethickness profile of the optical effective thickness in which anazimuthal section has two discontinuities of the optical effectivethickness can easily be realized, for example at θ=0° and θ=180°. Torealize the defined changes in magnitude of the specific rotation ofΔα=360°/(n·d) (if there a n angular segments 409 to form the element401), the individual sector elements 409 are preferably made of orcomprises cuvettes or cells, filled with an optical active liquid withthe required specific rotation α. As an example, for the m-th sectorelement the specific rotation is α(m)=α_(min)+m*360°/(n·d), and 0≦m≦n.The required specific rotation e.g. can be adjusted by the concentrationof the optical active material of the liquid, or by changing the liquidmaterial itself.

In a further embodiment the segments 409 of a polarization-modulatingoptical element 401 may comprise components of solid optically activematerial (like crystalline quartz) and cells or cuvettes filled withoptically active material, and these components are placed behind eachother in the light propagation direction. Alternative or in addition thecuvette itself may comprise optically active material like crystallinequartz.

The polarization-modulating optical element of the foregoing descriptionconverts linearly polarized incident light into a linear polarizationdistribution in which the oscillation planes of linearly polarized lightrays are rotated by an angle that depends on the thickness (or opticaleffective thickness) of each individual sector element. However, theangle by which the direction of polarization is rotated is constant overan individual sector element. Thus, the distribution function for thedirections of the oscillation planes of the individual field vectorstakes only certain discrete values.

A continuous distribution of linear polarizations can be achieved withan optical element that has a continuously varying thickness (opticaleffective thickness) profile along an azimuthal section.

An example of a continuously varying thickness profile is illustrated inFIG. 4 c. The azimuthal section 411 in this embodiment shows a lineardecrease in thickness (in general optical effective thickness) with aslope m=−180°/(α·π) over an azimuth-angle range of 0≦θ≦360°. Here theslope is defined a slope of a screw. Alternatively the slope can bedefined by m=−180°/(α*π*r) where r is the radius of a circle centered atthe element axis EA. In this case the slope depends on the distance ofthe element axis, e.g. if the polarization-modulating optical element301 has a given constant screw-slope (lead of a screw).

The symbol α in this context stands for the specific rotation of theoptically active crystal. As in the previously described embodiment ofFIG. 4 b, the thickness profile of FIG. 4 c has likewise a discontinuityat the azimuth angle θ=0°, the thickness of the polarization-modulatingoptical element 401 jumps from d_(min) to d_(max) by an amount ofapproximately 360°/α.

A further embodiment of a polarization-modulating optical element whichis shown in FIG. 4 d has a thickness profile (in general opticaleffective thickness profile) which is likewise suitable for producing acontinuous distribution of linear polarizations, in particular atangentially oriented polarization. This thickness profile correspondsto the embodiment shown in FIG. 3, in which the angle θ is measured incounterclockwise direction. The azimuthal section 411 in this embodimentis a linear function of the azimuth angle θ with a slope m=−180°/(α·n)over each of two ranges of 0<θ<180° and 180°<θ<360°. The thicknessprofile has discontinuities at θ=0° and θ=180° where the thickness risesabruptly from d_(min) to d_(max) by an amount of 180°/α.

FIG. 4 e represents the thickness profile (in general optical effectivethickness profile) along an azimuthal section for a further embodimentof the polarization-modulating optical element 401. The azimuthalsection is in this case a linear function of the azimuth angle θ with afirst slope m for 0<θ<180° and with a second slope n for 180°<θ<360°.The slopes m and n are of equal absolute magnitude but have oppositesigns. The respective amounts for m and n at a distance r from theelement axis are m=−180°/(α·π·r) and n=180°/(α·π·r). While thedifference between the minimum thickness d_(min) and the maximumthickness d_(max) is again approximately 180°/α, i.e., the same as inthe embodiment of FIG. 4 d, the concept of using opposite signs for theslope in the two azimuth angle ranges avoids the occurrence ofdiscontinuities.

Additionally it is mentioned that for certain special applicationsclockwise and counterclockwise optically active materials are combinedin a polarization-modulating optical element.

As the slope of the thickness profile along an azimuthal sectionincreases strongly with smaller radii, it is advantageous from amanufacturing point of view to provide a central opening 407 or acentral obscuration in a central portion around the central axis of thecircular polarization-modulating optical element.

It is furthermore necessary for reasons of mechanical stability todesign the polarization-modulating optical element with a minimumthickness d_(min) of no less than two thousandths of the elementdiameter. It is particularly advantageous to use a minimum thickness ofd_(min)=N·90°/α, where N is a positive integer. This design choiceserves to minimize the effect of birefringence for rays of an incidentlight bundle which traverse the polarization-modulating element at anangle relative to the optical axis.

FIG. 4 f schematically illustrates a further embodiment 421 of thepolarization-modulating optical element. As in FIG. 4 a, the elementaxis EA through the center of the polarization-modulating opticalelement 421 runs perpendicular to the plane of the drawing, and theoptical crystal axis runs parallel to the element axis. However, incontrast to the embodiments of FIGS. 3 and 4 a where thepolarization-modulating optical elements 301, 401 are made preferably ofone piece like in the case of crystalline material like crystallinequartz, the polarization-modulating optical element 421 comprises offour separate sector-shaped parts 422, 423, 424, 425 of an opticallyactive crystal material which are held together by a mounting device 426which can be made, e.g., of metal and whose shape can be described as acircular plate 427 with four radial spokes 428. The mounting ispreferably opaque to the radiation which is entering thepolarization-modulating optical element, thereby serving also as aspacer which separates the sector-shaped parts 422, 423, 424, 425 fromeach other. Of course the embodiment of the present invention accordingto FIG. 4 f is not intended to be limited to any specific shape and areaof mounting device 426, which may also be omitted.

According to an alternate embodiment not illustrated in FIG. 4 f,incident light which is entering the polarization-modulating opticalelement can also be selectively directed onto the sector-shaped parts,e.g. by means of a diffractive structure or other suitable opticalcomponents.

The sector-shaped parts 422 and 424 have a first thickness d1 which isselected so that the parts 422 and 424 cause the plane of oscillation oflinearly polarized axis-parallel light to be rotated by 90°+p·180°,where p represents an integer. The sector-shaped parts 423 and 425 havea second thickness d2 which is selected so that the parts 423 and 425cause the plane of oscillation of linearly polarized axis-parallel lightto be rotated by q·180°, where q represents an integer other than zero.Thus, when a bundle of axis-parallel light rays that are linearlypolarized in the y-direction enters the polarization-modulating opticalelement 421, the rays that pass through the sector-shaped parts 423 and425 will exit from the polarization-modulating optical element 421 withtheir plane of oscillation unchanged, while the rays that pass throughthe sector-shaped parts 422 and 424 will exit from thepolarization-modulating optical element 421 with their plane ofoscillation rotated into the x-direction. As a result of passing throughthe polarization-modulating optical element 421, the exiting light has apolarization distribution which is exactly tangential at the centerlines429 and 430 of the sector-shaped parts 422, 423, 424, 425 and whichapproximates a tangential polarization distribution for the rest of thepolarization-modulating optical element 421.

When a bundle of axis-parallel light rays that are linearly polarized inthe x-direction enters the polarization-modulating optical element 421,the rays that pass through the sector-shaped parts 423 and 425 will exitfrom the polarization-modulating optical element 421 with their plane ofoscillation unchanged, while the rays that pass through thesector-shaped parts 422 and 424 will exit from thepolarization-modulating optical element 421 with their plane ofoscillation rotated into the y-direction. As a result of passing throughthe polarization-modulating optical element 421, the exiting light has apolarization distribution which is exactly radial at the centerlines 429and 430 of the sector-shaped parts 422, 423, 424, 425 and whichapproximates a radial polarization distribution for the rest of thepolarization-modulating optical element 421.

Of course the embodiment of the present invention according to FIG. 4 fis not intended to be limited to the shapes and areas and the number ofsector-shaped parts exemplarily illustrated in FIG. 4 f, so that othersuitable shapes (having for example but not limited to trapeze-shaped,rectangular, square, hexagonal or circular geometries) as well as moreor less sector-shaped parts 422, 423, 424 and 425 can be used.Furthermore, the angles of rotation β₁ and β₂ provided by thesector-shaped parts 422, 423, 424, 425 (i.e. the correspondingthicknesses of the sector-shaped parts 422, 423, 424, 425) may be moregenerally selected to approximately conform to the expression|β₂−β₁|=(2n+1)·90°, with n representing an integer, for example toconsider also relative arrangements where incoming light is used havinga polarization plane which is not necessarily aligned with the x- ory-direction. With the embodiments as described in connection with FIG. 4f it is also possible to approximate polarization distributions with atangential polarization.

In order to produce a tangential polarization distribution from linearlypolarized light with a wave length of 193 nm and a uniform direction ofthe oscillation plane of the electric field vectors of the individuallight rays, one can use for example a polarization-modulating opticalelement of crystalline quartz with the design according to FIGS. 3 and 4d. The specific rotation α of quartz for light with a wavelength of 193nm is in the range of (325.2±0.5)°/mm, which was measured at awavelength of 180 nm, or more precise it is 321.1°/mm at 21.6° C. Thestrength and effect of the optical activity is approximately constantwithin a small range of angles of incidence up to 100 mrad. Anembodiment could for example be designed according to the followingdescription: An amount of 276.75 μm, which approximately equals 90°/α,is selected for the minimum thickness d_(min), if crystalline quartz isused Alternatively, the minimum thickness d_(min) can also be an integermultiple of this amount. The element diameter is 110 mm, with thediameter of the optically active part being somewhat smaller, forexample 105 mm. The base surface is designed as a planar surface asillustrated in FIG. 3. The opposite surface has a thickness profiled(r,θ) in accordance with FIG. 4 d. The thickness profile is defined bythe following mathematical relationships:

${D\left( {r,\theta} \right)} = {{276.75 + {{\frac{{180{^\circ}} - \theta}{180{^\circ}} \cdot 553.51}\mspace{11mu} {µm}\mspace{14mu} {for}\mspace{14mu} 0}} \leq \theta \leq {180{^\circ}}}$and $r > {\frac{10.5}{2}\mspace{11mu} {mm}}$${D\left( {r,\theta} \right)} = {{276.75 + {{\frac{{360{^\circ}} - \theta}{180{^\circ}} \cdot 553.51}\mspace{11mu} {µm}\mspace{14mu} {for}\mspace{14mu} 180}} \leq \theta \leq {360{^\circ}}}$and $r > {\frac{10.5}{2}\mspace{11mu} {mm}}$${D\left( {r,\theta} \right)} = {{0\mspace{25mu} {for}\mspace{14mu} r} \leq {\frac{10.5}{2}\mspace{11mu} {mm}}}$

The above mentioned data are based exemplarily for a specific rotation αof (325.2±0.5)°/mm. If the specific rotation α changes to 321.1°/mm, thevalue at 193 nm and at a temperature of 21.6° C., the thickness profilewill change as follows:

${D\left( {r,\theta} \right)} = {{278.6 + {{\frac{{180{^\circ}} - \theta}{180{^\circ}} \cdot 557}\mspace{11mu} {µm}\mspace{31mu} {for}\mspace{14mu} 0}} \leq \theta \leq {180{^\circ}\mspace{14mu} {and}\mspace{14mu} r} > {\frac{10.5}{2}\mspace{11mu} {mm}}}$${D\left( {r,\theta} \right)} = {{278.6 + {{\frac{{360{^\circ}} - \theta}{180{^\circ}} \cdot 557}\mspace{11mu} {µm}\mspace{20mu} {for}\mspace{14mu} 180}} \leq \theta \leq {360{^\circ}\mspace{14mu} {and}\mspace{14mu} r} > {\frac{10.5}{2}\; {mm}}}$${D\left( {r,\theta} \right)} = {{0\mspace{14mu} {for}\mspace{14mu} r} \leq {\frac{10.5}{2}\mspace{11mu} {mm}}}$

The polarization-modulating optical element according to this embodimenthas a central opening 407 with a diameter 10.5, i.e., one-tenth of themaximum aperture. The thickness maxima and minima, which are found atthe discontinuities, are 830.26 μm and 276.75 μm, respectively for thefirst given example.

The embodiment of the foregoing description can be produced with arobot-polishing process. It is particularly advantageous to produce thepolarization-modulating element from two wedge-shaped or helicallyshaped half-plates which are seamlessly joined together after polishing.If the element is produced by half-plates, it is easy and in someapplications of additional advantage to use one clockwise and onecounterclockwise optically active material like clockwise crystallineand counterclockwise crystalline quartz (R-quartz and L-quartz).

FIG. 5 schematically illustrates how a polarization-modulating opticalelement 501 with a thickness profile according to FIGS. 3 and 4 dconverts the polarization distribution of an entering light bundle 513with a uniformly oriented linear polarization distribution 517 into atangential polarization 519 of an exiting light bundle 515. This can bevisualized as follows: A linearly polarized light ray of the enteringlight bundle 513 which traverses the polarization-modulating opticalelement at a location of minimum thickness, for example at θ=180°,covers a distance of 90°/α inside the optically active crystal. Thiscauses the oscillation plane of the electrical field vector to berotated by 90°. On the other hand, a linearly polarized light raytraversing the polarization-modulating optical element 501 at a locationwith θ=45° covers a distance of 135°/α inside the optically activecrystal, thus the oscillation plane of the electrical field vector ofthis ray is rotated by 135°. Analogous conclusions can be drawn for eachlight ray of the entering light bundle 513.

FIG. 6 schematically illustrates how an optical arrangement with apolarization-modulating optical element 601 with a thickness profileaccording to FIGS. 3 and 4 d in combination with a furtherpolarization-modulating element 621 converts the polarizationdistribution of an entering light bundle 613 with a uniformly orientedlinear polarization distribution 617 into a radial polarization 623 ofan exiting light bundle 615. As explained in the context of FIG. 5, thepolarization-modulating optical element 601 produces a tangentialpolarization distribution. A tangential polarization distribution can beconverted into a radial polarization distribution by a 90°-rotation ofthe respective oscillation plane of each individual linearly polarizedray of the light bundle. There are several different possibilities toaccomplish this with an optical arrangement according to FIG. 6. Onepossible concept is to arrange a planar-parallel plate of an opticallyactive crystal as a further polarization-modulating element 621 in thelight path, where the thickness of the plate is approximately 90°/α_(p)with α_(p) representing the specific rotation of the optically activecrystal. As in the polarization-modulating element 601, the opticalcrystal axis of the planar parallel plate runs likewise parallel to theelement axis. As another possible concept, the furtherpolarization-modulating element 621 can be configured as a 90°-rotatorthat is assembled from two half-wave plates. A 90°-rotator consists oftwo half-wave plates of birefringent crystal material. Each plate has aslow axis associated with the direction of the higher refractive indexand, perpendicular to the slow axis, a fast axis associated with thedirection of the lower refractive index. The two half-wave plates arerotated relative to each other so their respective fast and slow axesare set at an angle of 45° from each other.

Of course further possible embodiments for producing a radialpolarization distribution are conceivable within the scope of theinvention. For example, the further polarization-modulating opticalelement 621 can be connected to the polarization-modulating opticalelement 601. To allow a fast change-over from tangential to radialpolarization, one could provide an exchange device that allows thefurther polarization-modulating element 621 to be placed in the lightpath and to be removed again or to be replaced by another element.

A tangential polarization distribution can also be produced with apolarization-modulating optical element that has a thickness profile inaccordance with FIG. 4 e. The thickness profile in this embodiment ofthe invention has no discontinuities. As visualized in FIG. 7 a, theuniformly oriented polarization distribution 717 of the entering lightbundle 713 is first transformed by the polarization-modulating opticalelement 701 into a linear polarization distribution 727 of an exitinglight bundle 715. The one-half of the entering light bundle 713 thatpasses through the polarization-modulating optical element 701 in theazimuth range 0≦θ≦180° of the thickness profile shown in FIG. 4 e isconverted so that the corresponding one-half of the exiting light bundlehas a tangential polarization distribution. The other half, however, hasa different, non-tangential polarization distribution 727. A furtherpolarization-modulating optical element is needed in the light path inorder to completely convert the polarization distribution 727 of thelight bundle 715 exiting from the polarization-modulating opticalelement 701 into a tangential polarization distribution 719. The furtherpolarization-modulating optical element is in this case configured as aplanar-parallel plate 725 with a first half 729 and a second half 731. Aplan view of the planar-parallel plate 725 is shown in FIG. 7 b. Thefirst half 729 is made of an isotropic material that has no effect onthe state of polarization of a light ray, while the second half 731 isdesigned as a half-wave plate. The planar-parallel plate 725 in theoptical arrangement of FIG. 7 a is oriented so that a projection RA′ ofthe reference axis RA of the polarization-modulating optical element 701onto the planar-parallel plate runs substantially along the separationline between the first half 729 and the second half 731. The slow axisLA of the birefringence of the half-wave plate is perpendicular to thisseparation line. Alternatively tangential polarization can also beachieved with a polarization-modulating optical element, having athickness profile as given by FIG. 4 e, if the element is composed oftwo half wedge-shaped or helically shaped elements of crystallinequartz, wherein the optical activity of one element is clockwise andthat of the other is counterclockwise. In this case no additionalplane-parallel plate 725 is necessary, as it is in the embodiment ofFIG. 7 a. In this embodiment preferably each wedge-shaped element has aconstant screw-slope, but the slopes have different directions as shownin the profile of FIG. 4 e. Further, it is not necessary that the slopesof the geometrical thickness d have the same absolute values, it issufficient if the slopes D of the optical effective thicknesses have thesame absolute values. In this case the specific rotations α aredifferent regarding absolute values for the two wedge-shaped elementswhich form the polarization-modulating optical element.

FIG. 8 schematically illustrates a microlithography projection system833 which includes the light source unit 835, the illumination system839, the mask 853 which carries a microstructure, the projectionobjective 855, and the substrate 859 that is being exposed to theprojection. The light source unit 835 includes a DUV- or VUV-laser, forexample an ArF laser for 192 nm, an F₂ laser for 157 nm, an Ar₂ laserfor 126 nm or a Ne₂ laser for 109 nm, and a beam-shaping optical systemwhich produces a parallel light bundle. The rays of the light bundlehave a linear polarization distribution where the oscillation planes ofthe electrical field vectors of the individual light rays are orientedin a uniform direction. The principal configuration of the illuminationsystem 839 is described in DE 195 29 563 (U.S. Pat. No. 6,258,433). Theparallel light bundle falls on the divergence-increasing optical element837. As a divergence-increasing optical element, one could use forexample a raster plate with an arrangement of diffractive or refractiveraster elements. Each raster element generates a light bundle whoseangle distribution is determined by the dimension and focal length ofthe raster element. The raster plate is located in or near the objectplane of an objective 840 that follows downstream in the light path. Theobjective 840 is a zoom objective which generates a parallel lightbundle with a variable diameter. A direction-changing mirror 841 directsthe parallel light bundle to an optical unit 842 which contains anaxicon (i.e., a rotationally symmetric prism arrangement) 843. The zoomobjective 840 in cooperation with the axicon 843 generates differentillumination profiles in the pupil plane 845, depending on the settingof the zoom and the position of the axicon elements. Apolarization-modulating optical element 801, for example of the kindshown in FIG. 3, is arranged in the pupil plane 845. Thepolarization-modulating optical element 801 is followed in the lightpath by a compensation plate 847 which has a thickness profile designedto compensate the angle deviations which the polarization-modulatingoptical element causes in the light rays that pass through it. Theoptical unit 842 is followed by a reticle-masking system (REMA) 849. TheREMA Objective 851 projects an image of the reticle-masking system 849onto the structure-carrying mask (reticle) 853, whereby the illuminatedarea of the reticle 853 is delimited. The projection objective 855projects the image of the structure-carrying mask 853 onto thelight-sensitive substrate 859. The space between the last opticalelement 857 of the projection objective and the light-sensitivesubstrate 859 contains an immersion liquid 861 with a refractive indexdifferent from air.

An additional advantage of the present invention is thatpolarization-modulating optical elements or the optical system accordingto the present invention can be used for adjusting the polarizationdistribution and also for temperature compensation of the polarizationdistribution in a microlithography projection system as described inFIG. 8. Advanced microlithography projection systems require in someapplications a predefined polarization distribution at the reticle 853with an accuracy of about 5° or even better, in some cases even betterthan 1°.

Since the polarization distribution at the reticle is influenced by thevarious optical elements by e.g. tension-induced birefringence, or byundefined or uncontrolled changes of the temperature of individualoptical elements, the polarization distribution can unpredictably oruncontrollably change over time. To correct such changes the temperaturedependency of the specific rotation α of the polarization-modulatingoptical element can be used to control the magnitude of the polarizationangles. The optical system according to an embodiment of the presentinvention preferably comprises a polarization control system forcontrolling the polarization distribution of the light beam which ispropagating through the optical system. The polarization distribution ofinterest is at a predefined location in the optical system. Thepolarization control system comprises at least one heating or coolingdevice to modify the temperature and/or the temperature distribution ofthe polarization-modulating optical element to affect the polarizationdistribution of the light beam at the predefined location. Here thepolarization-modulating optical element may have a varying or constanteffective optical thickness.

In the case of a constant effective optical thickness the optical systemcomprises an optical axis or a preferred direction given by thedirection of a light beam propagating through the optical system. Theoptical system additionally comprises a polarization-modulating opticalelement described by coordinates of a coordinate system, wherein onepreferred coordinate of the coordinate system is parallel to the opticalaxis or parallel to said preferred direction. Thepolarization-modulating optical element comprises solid and/or liquidoptically active material, wherein the effective optical thickness isconstant as a function of at least one coordinate different from thepreferred coordinate of the coordinate system. The optical systemcomprises further a polarization control system for controlling thepolarization distribution of the light beam (propagating through theoptical system) at a predefined location in the optical system, and thepolarization control system comprises at least one heating or coolingdevice to modify the temperature and/or the temperature distribution ofthe polarization-modulating optical element to affect the polarizationdistribution of the light beam at the predefined location.

As an example, if the polarization-modulating optical element (as usede.g. in the optical system according to the present invention) is madeof synthetic (crystalline) quartz, comprising a parallel plate or formedas a parallel plate, a thickness of 10 mm of such a plate will result ina change of polarization of 23.6 mrad/° C. or 23.6 mrad/K, equivalent to1.35°/K, due to the linear temperature coefficient γ of the specificrotation α with γ=2.36 mrad/(mm*K). These data correspond to awavelength of 193 nm. In such an embodiment, which is schematicallyshown in FIG. 9, the optical axis OA of the parallel plate 901 isdirected parallel or approximately parallel to the propagation of thelight (indicated by reference numeral 950) in the optical system.Approximately parallel means that the angle between the optical axis OAof the parallel plate 901 and the direction of the light propagatingthrough the optical system is smaller than 200 mrad, preferably smallerthan 100 mrad or even smaller than 50 mrad. Controlling the temperatureof the plate 901 will result in a controlled change of polarization. Iffor example the temperature of the plate will be controlled in a rangeof about 20° C. to 40° C., the polarization angles can be controllablychanged in a range of about ±13.5° for such a plate 901 made of quartz.This high sensitivity allows a control of the polarization distributionby temperature control. In such a case even a plane plate with athickness d of about 0.1 mm up to 20 mm will become apolarization-modulating optical element 901, able to controllably adjusta polarization distribution by controlling the temperature of the plate901. Preferably for synthetic (crystalline) quartz the thickness of theplate 901 is n*278.5 μm (n is any integer) which results in a rotationof a polarization plane of at least 90° for n=1 and 180° for n=2 and ingeneral n*90°, for a wavelength of 193 nm at about 21.6° C. For a 90°rotation of the polarization plane the synthetic quartz should be atleast 278.5 μm thick and for 180° at least 557.1 μm, for 270° thethickness should be 835.5 μm and for a 360° rotation of the polarizationthe thickness is 1.114 mm. The manufacturing tolerances regardingthickness are about ±2 μm. Thus the manufacturing tolerance results inan inaccuracy of the angle of the polarization plane of the light whichpasses the plate of about ±0.64° at about 21.6° C. and 193 nm. To thisinaccuracy an additional inaccuracy caused by temperature fluctuation ofthe plate (or polarization-modulating optical element) have to beconsidered, which is given by the linear temperature coefficient γ ofthe specific rotation α with is γ=2.36 mrad/(mm*K)=0.15°/(mm*K).

The temperature control of the plate 901 can be done by closed-loop oropen-loop control, using a temperature sensing device with at least onetemperature sensor 902, 903 for determining the temperature of the plate901 (or providing a temperature sensor value which is representative orequal to the temperature and/or the temperature distribution of thepolarization-modulating optical element), at least a heater 904, 905,preferably comprising an infrared heater, for heating the plate byinfrared radiation 906, and a control circuit 910 for controlling the atleast one heater 904, 905. As an example of a temperature sensing devicea infrared sensitive CCD-element with a projection optics may be used,wherein the projection optics images at least a part of the plate 901onto the CCD-element such that a temperature profile of the viewed partof the plate 901 can be determined by the analysis of the CCD-elementsignals. The control circuit 910 may comprise a computer system 915 ormay be connected to the computer or control system 915 of themicrolithography projection system 833 (see FIG. 8). In a preferredembodiment of the temperature controlled plate 901 the thickness ischosen such that a rotation of the polarization of n*90°, n is anyinteger number, is achieved at a temperatureT=(T_(max)−T_(min))/2+T_(min), whereas T_(max) and T_(min), are themaximum and minimum temperatures of the plate 901 (or in general thepolarization-manipulating optical element). Preferably the heater orheating system (and also any cooling device like a Peltier element) isarranged such that it is not in the optical path of the microlithographyprojection system 833, or that it is not in the optical path of thelight beam which is propagating through the optical system according toan embodiment of the present invention. Preferably the optical systemwith the polarization control system according to the present inventionis used in a system with at least one additional optical elementarranged between the polarization-modulating optical element and thepredefined location in the optical system such that the light beamcontacts the at least one additional optical element when propagatingfrom the polarization-modulating optical element to the predefinedlocation. The additional optical element preferably comprises a lens, aprism, a mirror, a refractive or a diffractive optical element or anoptical element comprising linear birefringent material. Thus theoptical system according to the present invention may form a part of amicrolithography projection system 833.

In a further preferred embodiment the temperature of thepolarization-manipulating optical element 901 (the plate as shown inFIG. 9) corresponds to a predefined temperature profile. As an example,such a temperature profile is achieved by using a plurality of infraredheaters 904, 905 to produce a radiation distribution across the opticalelement 901 which heats the optical element 901 in a controlled way witha control circuit as already described. In such an embodiment also aplurality of temperature sensors 902, 903 can be used for the controlcircuit 910. With this embodiment the polarization state in a fieldplane or pupil plane of the microlithography projection system 833 canbe adjusted locally.

Alternatively or in addition the heater or heating elements 904, 905 maybe replaced or supplemented by one or more Peltier-elements 907, 908.The Peltier-element or elements are preferably connected to the controlcircuit 910 such that a control by open and/or closed loop control ispossible. The advantage of the Peltier-elements is that also acontrolled cooling of the polarization-manipulating optical element 901can be achieved. Heating and cooling the optical element 901 at the sametime result in complex temperature distributions in thepolarization-modulating optical element 901, which result in complexpolarization distributions of the light 950 propagating e.g. through themicrolithography projection system 833, after passing the element 901.Of course, other heating and cooling means than the ones mentioned abovecan be used to achieve a required temperature profile or a requiredtemperature of the polarization-modulating optical element 901.

The application of the plane plate 901 as polarization-modulatingoptical element 801 in the illumination system of a microlithographyprojection apparatus 833 (see FIG. 8) is preferably in the pupil plane845 and/or at positions between the light source unit 835 and thementioned pupil plane 845. Applying the plane plate 901 at theselocations has the advantage that the angle of incidence of the lightwhich passes through the plate 901 and also passing through themicrolithography projection apparatus is smaller than about 6° (100mrad). At these small angles the influence of linear birefringence,caused by the plate 901, is very small such that the polarization of thelight after passing the plate 901 is almost liner with negligibleelliptical parts, if the light was linearly polarized before enteringthe plate 901.

In a further preferred embodiment of the invention the state of thepolarization of the light passed through the polarization-modulatingelement 901 or the optical system according to the present invention ismeasured. For this the polarization control system comprises apolarization measuring device providing a polarization valuerepresentative for or equal to the polarization or the polarizationdistribution of the light beam at the predetermined location in theoptical system. Further, the control circuit controls the at least oneheating or cooling device dependent on the temperature sensor valueand/or the polarization value by open or closed loop control. Themeasured state of polarization is compared with a required state and inthe case that the measured state deviates more than a tolerable value,the temperature and/or the temperature distribution of thepolarizing-modulating element like the plane plate 901 is changed suchthat the difference between the measured and the required state ofpolarization becomes smaller, and if possible such small that thedifference is within a tolerable value. In FIG. 9 the measurement of thestate of polarization is measured in-situ or with a separate specialmeasurement, depending on the polarization measuring device 960. Thepolarization measuring device may be connected with the control circuit910, such that depending on the measured polarization state values theheating means 904, 905 and/or 907, 908 are controlled heated and/orcooled such that the measured and the required state of polarizationbecomes smaller. The control can be done in open or closed loop modus.

The plane plate 901 used as polarization-modulating optical element orbeing a part of such element is especially appropriate to correctorientations of polarization states of the passed light bundles.

In a further embodiment of the present invention the plane plate 901(comprising or consisting of optically active material), used as apolarization-modulating optical element, is combined with a plate 971(see FIG. 10), comprising or consisting of linear birefringent material.With this embodiment of the invention the orientation and the phase ofthe passing light bundle 950 can be subjected such that e.g. a planepolarized light bundle becomes elliptically polarized after passing bothplane plates 901 and 971, or vice versa. In this embodiment at least oneplate 901 or 971 is controlled regarding its temperature and/ortemperature distribution as described in connection with FIG. 9.Further, the sequence of the plates 901 and 971 may be changed such thatthe passing light bundles are first passing through the plate 971,comprising or consisting of linear birefringent material, and thanthrough the plate 901, comprising or consisting of optical activematerial, or vice versa. Preferably both plates are consecutivelyarranged along the optical axis OA of the system. Also, more than oneplate comprising or consisting of linear birefringent material, and/ormore than one plate comprising or consisting of optical active materialmay be used to manipulate the state of polarization of the passing lightbundles. Further, a plane plate 971, or 901 may be exchanged by a liquidcell or cuvette containing optically active material. Also the planeplates 971, comprising or consisting of linear birefringent material,and plate 901, comprising or consisting of optical active material, canbe arranged such that at least one other optical element 981 is placedbetween these plane plates. This element 981 can be for example a lens,a diffractive or refractive optical element, a mirror or an additionalplane plate.

In an additional embodiment of the present invention apolarization-modulating element or in general a polarizing opticalelement is temperature compensated to reduce any inaccuracy of thepolarization distribution generated by the polarization-modulatingelement due to temperature fluctuations of said element, which forsynthetic quartz material is given by the linear temperature coefficientγ of the specific rotation α for quartz (which is as already mentionedabove γ=2.36 mrad/((mm*K)=0.15°/(mm*K)). The temperature compensationmakes use of the realization that for synthetic quartz there exist onequartz material with a clockwise and one quartz material with acounterclockwise optical activity (R-quartz and L-quartz). Both, theclockwise and the counterclockwise optical activities are almost equalin magnitude regarding the respective specific rotations α. Thedifference of the specific rotations is less than 0.3%. Whether thesynthetic quartz has clockwise (R-quartz) or counterclockwise (L-quartz)optical activity dependents on the seed-crystal which is used in themanufacturing process of the synthetic quartz.

R- and L-quartz can be combined for producing a thermal or temperaturecompensated polarization-modulating optical element 911 as shown in FIG.11. Regarding the change of the state of polarization such a temperaturecompensated polarization-modulating optical element 911 is equivalent toa plane plate of synthetic quartz of thickness d. For example, two planeplates 921 and 931 are arranged behind each other in the direction 950of the light which is propagating through the optical system whichcomprises the temperature compensated polarization-modulating opticalelement 911. The arrangement of the plates is such that one plate 931 ismade of R-quartz with thickness d_(R), and the other 921 is made ofL-quartz with thickness d_(L), and |d_(R)−d_(L)|=d. If the smallerthickness of d_(R) and d_(L) (min(d_(R), d_(L))) is larger than d ormin(d_(R), d_(L))>d, which in most cases is a requirement due tomechanical stability of the optical element, then the temperaturedependence of the polarization state becomes partly compensated, meaningthat the temperature dependence of the system of R-quartz and L-quartzplates is smaller than γ=2.36 mrad/(mm*K)*d=0.15°/(mm*K)*d, wherein d isthe absolute value of the difference of the thicknesses of the twoplates d=|d_(R)−d_(L)|. The following example demonstrates this effect.A R-quartz plate 931 with a thickness of e.g. d_(R)=557.1 μm (resultingin a 180° clockwise change of the exiting polarization plane compared tothe incident polarization plane) is combined with a L-quartz plate 921with a thickness of d_(L)=557.1 μm+287.5 μm (resulting in a 2700counterclockwise change of the exiting polarization plane compared tothe incident polarization). This result in a 90° counterclockwise changeof the polarization plane after the light pass both plane plates 921,931, corresponding to a 270° clockwise change of the polarization planeif just a R-quartz plate would be used. In this case the temperaturecompensation is not fully achieved, but it is reduced to value of about0.04°/K if both plates are used, compared to 0.13°/K if just a R-quartzplate of d_(R)=557.1 μm+287.5 μm would be used. This is a significantreduction of temperature dependency, since even if the temperature willchange by 10° C. the change of the polarization plane is still smallerthan 1°.

In general any structured polarization-modulating optical element madeof R- or L-quartz, like e.g. the elements as described in connectionwith FIGS. 3 and 4 a can be combined with a plane plate of therespective other quartz type (L- or R-quartz) such that the combinedsystem 911 will have a reduced temperature dependence regarding thechange of the polarization. Instead of the plane plate also a structuredoptical element made of the respective other quartz type may be usedsuch that in FIG. 11 the shown plates 921 and 931 can be structuredpolarization-modulating optical elements as mentioned in thisspecification, having specific rotations of opposite signs, changing thestate of polarization clockwise and counterclockwise.

To generalize the above example of a temperature compensatedpolarization-modulating optical element 911, the present invention alsorelates to an optical system comprising an optical axis OA or apreferred direction 950 given by the direction of a light beampropagating through the optical system. The optical system comprising atemperature compensated polarization-modulating optical element 911described by coordinates of a coordinate system, wherein one preferredcoordinate of the coordinate system is parallel to the optical axis OAor parallel to said preferred direction 950. The temperature compensatedpolarization-modulating optical element 911 comprises a first 921 and asecond 931 polarization-modulating optical element. The first and/or thesecond polarization-modulating optical element comprising solid and/orliquid optically active material and a profile of effective opticalthickness, wherein the effective optical thickness varies at least as afunction of one coordinate different from the preferred coordinate ofthe coordinate system. In addition or alternative the first 921 and/orthe second 931 polarization-modulating optical element comprises solidand/or liquid optically active material, wherein the effective opticalthickness is constant as a function of at least one coordinate differentfrom the preferred coordinate of the coordinate system. As an additionalfeature, the first and the second polarization-modulating opticalelements 921, 931 comprise optically active materials with specificrotations of opposite signs, or the first polarization-modulatingoptical element comprises optically active material with a specificrotation of opposite sign compared to the optically active material ofthe second polarization-modulating optical element. In the case of planeplates, preferably the absolute value of the difference of the first andthe second thickness of the first and second plate is smaller than thethickness of the smaller plate.

In an additional embodiment of the present invention apolarization-modulating element comprises an optically active and/oroptically inactive material component subjected to a magnetic field suchthat there is a field component of the magnetic field along thedirection of the propagation of the light beam through thepolarization-modulating element. The optical active material componentmay be construed as described above. However, also optical inactivematerials can be used, having the same or similar structures asdescribed in connection with the optical active materials. Theapplication of a magnetic field will also change the polarization stateof the light passing through the optical active and/or optical inactivematerial due to the Faraday-effect, and the polarization state can becontrolled by the magnetic field.

Various embodiments for a polarization-modulating optical element or forthe optical systems according to the present invention are described inthis application. Further, also additional embodiments ofpolarization-modulating optical elements or optical systems according tothe present invention may be obtained by exchanging and/or combiningindividual features and/or characteristics of the individual embodimentsdescribed in the present application.

1. An optical element, comprising: a polarization-modulating opticalelement comprising an optically active crystal having an optical axis,the polarization-modulating optical element having a thickness profilethat, as measured in the direction of the optical axis, is variable,wherein the polarization-modulating optical element has an element axisoriented substantially in the direction of the optical axis of theoptically active crystal, and the thickness profile in relation to theelement axis has a variation that depends only on an azimuth angle θ,where θ is measured from a reference axis that runs perpendicular to theelement axis and intersects the element axis.
 2. The optical element ofclaim 1, wherein the thickness profile has a constant value along aradius that is oriented perpendicularly to the element axis and at theangle θ relative to the reference axis.
 3. The optical element of claim1, wherein the polarization-modulating optical element is configured totransform an entering light bundle with a first linear polarizationdistribution into an exiting light bundle with a second linearpolarization distribution different from the first linear polarizationdistribution.
 4. The optical element of claim 3, wherein the secondlinear polarization distribution is an approximately tangentialpolarization distribution or an approximately radial polarizationdistribution.
 5. The optical element of claim 1, wherein an azimuthalsection of the thickness profile in a range of azimuth angles 10°<θ<350°and at a constant distance r from the element axis is a linear functionof the azimuth angle θ, and the azimuthal section has a slope mconforming approximately to the expression${{m} = \frac{180{^\circ}}{{\alpha\Pi}\; r}},$ with α representingthe specific rotation of the optically active crystal.
 6. The opticalelement of claim 5, wherein the azimuthal section has a substantiallyjump-like increase of 360°/α at the azimuth angle θ=0°.
 7. The opticalelement of claim 1, wherein an azimuthal section of the thicknessprofile in a range of azimuth angles 10°<θ<170° and 190°<θ<350° at aconstant distance r from the element axis is a linear function of theazimuth angle θ, wherein this azimuthal section has a slope m conformingapproximately to the expression${{m} = \frac{180{^\circ}}{{\alpha\Pi}\; r}},$ with α representingthe specific rotation of the optically active crystal.
 8. The opticalelement of claim 7, wherein the azimuthal section has a substantiallyjump-like increase of 180°/α at the azimuth angles θ=0° and θ=180°. 9.The optical element of claim 1, wherein an azimuthal section of thethickness profile at a constant distance r from the element axis and ina first azimuth angle range of 10°<θ<170° is a linear function of theazimuth angle θ with a first slope m, while in a second azimuth anglerange of 190°<θ<350°, the azimuthal section is a linear function of theazimuth angle θ with a second slope n, wherein the slopes m and n havethe same absolute magnitude but opposite signs, and wherein themagnitude of the slopes m and n conforms to the expression${m} = {{n} = \frac{180{^\circ}}{{\alpha\Pi}\; r}}$ with αrepresenting the specific rotation of the optically active crystal. 10.The optical element of claim 1, wherein the polarization-modulatingoptical element comprises at least two planar-parallel portions ofdifferent thickness or different optical effective thickness.
 11. Theoptical element of claim 10, wherein the at least two planar-parallelportions are configured as sectors of a circle, or as hexagonal, square,rectangular, or trapeze-shaped raster elements and/or comprise at leasta cuvette comprising an optically active or optically inactive liquid.12. The optical element of claim 10, wherein a first pair ofplan-parallel portions are arranged on opposite sides of a centralelement axis of the polarization-modulating optical element, a secondpair of plan-parallel portions are arranged on opposite sides of theelement axis and circumferentially displaced around the element axiswith respect to the first pair of plan-parallel portions, and each ofthe first portions has a thickness or optical effective thicknessdifferent from a thickness or optical effective thickness of each of thesecond portions.
 13. The optical element of claim 12, wherein, whenlinearly polarized light passes through the optical element, a plane ofoscillation of the linearly polarized light passing is rotated by afirst angle of rotation β₁ within at least one of the firstplan-parallel portions and by a second angle of rotation β₂ within atleast one of the second plan-parallel portions, where β₁ and β₂ areapproximately conforming to the expression |β₂−β₁|=(2n+1) 90°, with nrepresenting an integer.
 14. The optical element of claim 13, wherein β₁and β₂ are approximately conforming to the expressions β₁=90°+p·180°,with p representing an integer, and β₂=q·180°, with q representing aninteger other than zero.
 15. The optical element of claim 12, whereinthe second pair of plan-parallel portions is circumferentially displacedaround the element axis with respect to first pair of plan-parallelportions by approximately 90°.
 16. The optical element of claim 12,wherein the first pair of plan-parallel portions and said second pair ofplan-parallel portions are arranged on opposite sides of a centralopening or a central obscuration of the polarization-modulating opticalelement.
 17. The optical element of claim 12, wherein adjacent portionsof the first and second pairs are spaced apart from each other byregions being opaque or not optically active to linearly polarized lightentering the polarization-modulating optical element.
 18. The opticalelement of claim 12, wherein the portions of the first and second pairare held together by a mounting.
 19. The optical element of claim 18,wherein the mounting is opaque or not optically active to linearlypolarized light entering the polarization-modulating optical element.20. The optical element of claim 18, wherein the mounting has asubstantially spoke-wheel shape.
 21. The optical element of claim 10,further comprising: a first group of substantially planar-parallelportions; and a second group of substantially planar-parallel portions,wherein: when linearly polarized light passes through the opticalelement, a plane of oscillation of the linearly polarized light isrotated by a first angle of rotation β₁ by the first group ofsubstantially planar-parallel portions, when linearly polarized lightpasses through the optical element, a plane of oscillation of thelinearly polarized light is rotated by a second angle of rotation β₂ bythe second group of substantially planar-parallel portions, and β₁ andβ₂ are approximately conforming to the expression |β₂−β₁|=(2n+1) 90°,with n representing an integer.
 22. The optical element of claim 21,wherein β₁ and β₂ are approximately conforming to the expressionsβ₁=90°+p·180°, with p representing an integer, and β₂=q·180°, with qrepresenting an integer other than zero.
 23. The optical element ofclaim 1, wherein the thickness profile or profile of effective opticalthickness has a continuous shape.
 24. The optical element of claim 1,further comprising an element diameter and a minimal thickness, whereinthe minimal thickness of the element is at least equal to 0.002 timesthe diameter of the element.
 25. The optical element of claim 1, whereinthe thickness profile has a minimal thickness${d_{\min} = {N \cdot \frac{90{^\circ}}{\alpha}}},$ with α representingthe specific rotation of the optically active crystal and N representinga positive integer.
 26. The optical element of claim 1, wherein thepolarization-modulating optical element has a central opening or acentral obscuration.
 27. The optical element of claim 1, wherein thepolarization-modulating optical element is configured to transform anentering light bundle with a first linear polarization distribution intoan exiting light bundle with a second linear polarization distribution,wherein the entering light bundle consists of a multitude of light rayswith an angle distribution relative to the optical axis of the opticallyactive crystal, and the angle distribution has a maximum angle ofincidence not exceeding 100 mrad.
 28. An optical arrangement,comprising: the polarization-modulating optical element according ofclaim 1; and a second polarization-modulating optical element arrangedso that, when light passes through the optical arrangement, the lightcan pass through the first and second polarization-modulating elements.29. The optical arrangement of claim 28, wherein the secondpolarization-modulating optical element comprises apolarization-modulating optical element in accordance with claim
 1. 30.The optical arrangement of claim 28, wherein the secondpolarization-modulating optical element comprises a planar-parallelplate of an optically active crystal and/or a cuvette with opticallyactive or optically inactive liquid.
 31. The optical arrangement ofclaim 28, wherein the second polarization-modulating optical elementcomprises a rotator made of two half-wavelength plates that are rotatedby 45° relative to each other.
 32. The optical arrangement of claim 28,wherein: the first polarization-modulating optical element has anelement axis in reference to which the thickness profile has a variationthat depends only on an azimuth angle θ, wherein the azimuth angle θ ismeasured from a reference axis that is oriented perpendicular to theelement axis and intersects the element axis; the thickness profile in afirst azimuth angle range of 10°<θ<170° is a linear function of theazimuth angle θ with a first slope m, while in a second azimuth anglerange of 190°<θ<350° the azimuthal section is a linear function of theazimuth angle θ with a second slope n, wherein the slopes m and n havethe same absolute magnitude but opposite signs; and the secondpolarization-modulating optical element comprises a planar-parallelplate which is configured as a half-wavelength plate for a half-spacethat covers an azimuth-angle range of 180°.
 33. The optical arrangementof claim 28, wherein the second polarization-modulating optical elementcauses a 90°-rotation of the oscillation plane of a linearly polarizedlight ray passing through the optical arrangement.
 34. The opticalarrangement of claim 28, further comprising a compensation plate in thelight path of the optical system, the compensation plate having athickness profile configured to substantially compensate the angledeviations of transmitted radiation which are caused by the firstpolarization-modulating optical element.
 35. A system, comprising: anillumination system; a projection objective; and the optical element ofclaim 1 in the illumination system, wherein the system is amicrolithography optical system.
 36. A system, comprising: anillumination system; a projection objective; and the optical arrangementof claim 28 in the illumination system, wherein the system is amicrolithography optical system.
 37. The system of claim 36, furthercomprising: a substrate; and an immersion medium with a refractive indexdifferent from air is between the substrate and an optical elementnearest to the substrate.
 38. A method, comprising manufacturing amicro-structured semiconductor component using a system in accordancewith claim
 35. 39. A system, comprising: an illumination system; aprojection objective; and a polarization-modulating optical elementcomprising an optically active crystal having an optical axis, thepolarization-modulating optical element having a thickness profile that,as measured in the direction of the optical axis, is variable; whereinthe system is a microlithography optical system; and wherein thepolarization-modulating optical element is arranged in a pupil plane ofthe illumination system.
 40. The system of claim 39, wherein thepolarization-modulating optical element has an element axis orientedsubstantially in the direction of the optical axis of the opticallyactive crystal, and the thickness profile in relation to the elementaxis has a variation that depends only on an azimuth angle θ, where θ ismeasured from a reference axis that runs perpendicular to the elementaxis and intersects the element axis.
 41. The system of claim 40,wherein the thickness profile has a constant value along a radius thatis oriented perpendicularly to the element axis and at the angle θrelative to the reference axis.
 42. The system of claim 39, wherein thepolarization-modulating optical element is configured to transform anentering light bundle with a first linear polarization distribution intoan exiting light bundle with a second linear polarization distributiondifferent from the first linear polarization distribution.
 43. Thesystem of claim 42, wherein the second linear polarization distributionis an approximately tangential polarization distribution or anapproximately radial polarization distribution.
 44. An optical element,comprising: a polarization-modulating optical element comprising anoptically active crystal having an optical axis, thepolarization-modulating optical element having a thickness profile that,as measured in the direction of the optical axis, is variable, whereinthe polarization-modulating optical element is configured to transforman entering light bundle with a first linear polarization distributioninto an exiting light bundle with a second linear polarizationdistribution different from the first linear polarization distribution,and the second linear polarization distribution is an approximatelyradial polarization distribution.